As mentioned above, in the literature there exist several approaches to investigate the inhomogeneities of the universe.
Such approaches can be generalized to the modified LQC models, including mLQC-I and mLQC-II. In this section we shall focus ourselves
on cosmological perturbations in the framework of mLQCs following the dressed metric approach [1]}, [2]}, [3]}, while in the next section we will be following the hybrid approach
[4]}, [5]}, [6]}, [7]}, [8]}. We shall restrict ourselves to the effective dynamics, as we did with the homogeneous
background in the last section. Such investigations in general include two parts: (a) the initial conditions; and (b) the dynamical evolutions of perturbations. In the framework of
effective dynamics, the latter is a second-order ordinary differential equation in the momentum space, so in principle once the initial conditions are given, it uniquely determines
the cosmological (scalar and tensor) perturbations.
